{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "N=21;\n",
    "x=range(-2, 2, N);\n",
    "dx = (2-(-2))/(N-1);\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# f = x.^2 .+ 1;\n",
    "f = sin.(x)\n",
    "@show [x f]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(x, f)\n",
    "scatter!(x, f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "df_exact = Array{Float64}(undef, N);\n",
    "\n",
    "# df_exact = 2 .* x;\n",
    "df_exact = cos.(x);\n",
    "\n",
    "df_front = Array{Float64}(undef, N);\n",
    "df_back  = Array{Float64}(undef, N);\n",
    "df_center  = Array{Float64}(undef, N);\n",
    "\n",
    "for i in 2:N-1\n",
    "    df_front[i] = (f[i] - f[i-1])/dx\n",
    "    df_back[i] = (f[i+1] - f[i])/dx\n",
    "    df_center[i] = (f[i+1] - f[i-1])/(2.0*dx)\n",
    "end\n",
    "\n",
    "# df_front[1] = (f[2] - f[1])/dx;\n",
    "# df_back[1] = (f[2] - f[1])/dx;\n",
    "# df_center[1] = (f[2] - f[1])/dx;\n",
    "df_front[1] = (f[2] - f[1])/dx;\n",
    "df_back[1] = (f[2] - f[1])/dx;\n",
    "df_center[1] = (-f[3] +4.0*f[2] -3.0* f[1])/(2.0*dx);\n",
    "\n",
    "\n",
    "df_front[N] = (f[N] - f[N-1])/dx;\n",
    "df_back[N] = (f[N] - f[N-1])/dx;\n",
    "df_center[N] = (f[N] - f[N-1])/dx;\n",
    "\n",
    "# plot(x, df_exact, ylims =(0.5,0.7), xlims = (0.9, 1.1), label = \"exact\")\n",
    "plot(x, df_exact, label = \"exact\")\n",
    "plot!(x, df_front, label = \"front\")\n",
    "plot!(x, df_back, label = \"back\")\n",
    "plot!(x, df_center, label = \"center\")\n",
    "scatter!(x, df_center, label = \"center\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实验： 验证不同方法求解热传导方程的效果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "using LinearAlgebra\n",
    "using SparseArrays\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dt / dx ^ 2 = 0.4901960784313725\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.4901960784313725"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#定义计算域 \n",
    "Nx = 6;\n",
    "x=range(0, 1, Nx);\n",
    "\n",
    "Nt = 50;\n",
    "t = range(0, 1, Nt);\n",
    "\n",
    "dx = 1.0/(Nx -1);\n",
    "dt = 1.0/(Nt-1);\n",
    "\n",
    "#给初值\n",
    "function ic(x)\n",
    "   return x^3 + x\n",
    "end\n",
    "\n",
    "#给边界条件\n",
    "function bc0(t)\n",
    "   return 0.0e0\n",
    "end \n",
    "function bcn(t)\n",
    "   return 1.0e0+exp(t)\n",
    "end\n",
    "\n",
    "#源项\n",
    "function source(x, t)\n",
    "   return x*exp(t) - 6.0*x\n",
    "end\n",
    "\n",
    "#求解\n",
    "\n",
    "function exact(x, t)\n",
    "   T = Array{Float64}(undef, Nx, Nt)\n",
    "   for n in 1:Nt\n",
    "      for i in 1:Nx\n",
    "         T[i, n] = x[i]*(x[i]^2+exp(t[n]));\n",
    "      end\n",
    "   end\n",
    "   return T;\n",
    "end\n",
    "\n",
    "function Euler(x, t)\n",
    "   T = Array{Float64}(undef, Nx, Nt)\n",
    "   T[:, 1] = ic.(x);\n",
    "   lambda = dt/dx^2;\n",
    "   n = 2\n",
    "   while n<=Nt\n",
    "      T[1, n] = bc0.(t[n]);\n",
    "      T[end, n] = bcn.(t[n]);\n",
    "      for i in 2:Nx-1\n",
    "         T[i, n] = T[i, n-1] + lambda * (T[i-1, n-1] - 2*T[i, n-1] + T[i+1, n-1]) + dt*source(x[i], t[n-1]);\n",
    "      end\n",
    "      n = n+1\n",
    "   end\n",
    "   return T;\n",
    "end\n",
    "\n",
    "function cn(x, t)\n",
    "   T = Array{Float64}(undef, Nx, Nt);\n",
    "   A = sparse(zeros(Nx-2, Nx-2)); \n",
    "   rhs = Array{Float64}(undef, Nx-2); rhs .= 0.0e0;\n",
    "\n",
    "   T[:, 1] = ic.(x);\n",
    "   T[1, :] = bc0.(t);\n",
    "   T[end, :] = bcn.(t);\n",
    "   lambda = 0.5*dt/dx^2;\n",
    "   for i in 2:Nx-1\n",
    "      A[i-1, i-1] = 2.0*lambda +1.0e0;\n",
    "   end\n",
    "   for i in 2:Nx-2\n",
    "      A[i-1, i] = -lambda;\n",
    "   end\n",
    "   for i in 3:Nx-1\n",
    "      A[i-1, i-2] = -lambda;\n",
    "   end\n",
    "\n",
    "   n=2\n",
    "\n",
    "   while n<=Nt\n",
    "      T[1, n] = bc0.(t[n]);\n",
    "      T[end, n] = bcn.(t[n]);\n",
    "      for i in 2:Nx-1\n",
    "         rhs[i-1] = T[i, n-1] + dt*source(x[i], 0.5*(t[n] + t[n-1])) + lambda*(T[i-1, n-1] - 2*T[i, n-1] + T[i+1, n-1]);\n",
    "      end\n",
    "      rhs[1] = rhs[1]+lambda*T[1, n];\n",
    "      rhs[end] = rhs[end]+lambda*T[end, n];\n",
    "      T[2:end-1, n] = A\\rhs;\n",
    "\n",
    "      n=n+1\n",
    "   end\n",
    "   return T\n",
    "end\n",
    "\n",
    "@show dt/dx^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#exact\n",
    "\n",
    "T_exact = exact(x, t)\n",
    "#Euler\n",
    "T_Euler=Euler(x, t);\n",
    "T_cn = cn(x, t);\n",
    "# plot(x, T_cn.-T_exact)\n",
    "plot(x, T_Euler[:, end].-T_exact[:, end], label=\"Euler\")\n",
    "# plot!(x, T_exact[:, end], label=\"exact\")\n",
    "plot!(x, T_cn[:, end].-T_exact[:, end], label=\"cn\")\n",
    "\n",
    "# @show norm(T_Euler.-T_exact), norm(T_cn.-T_exact);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(norm(T_Euler .- T_exact), norm(T_cn .- T_exact)) = (5.0466761813137844e160, 4.804163246337204e-6)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(5.0466761813137844e160, 4.804163246337204e-6)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@show norm(T_Euler.-T_exact), norm(T_cn.-T_exact)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, T_Euler[:, end])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A = sparse([1, 2, 1, 2, 3, 2, 3, 4, 3, 4], [1, 1, 2, 2, 2, 3, 3, 3, 4, 4], [1.5, -0.24999999999999994, -0.24999999999999994, 1.5, -0.24999999999999994, -0.24999999999999994, 1.5, -0.24999999999999994, -0.24999999999999994, 1.5], 4, 4)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4×4 SparseMatrixCSC{Float64, Int64} with 10 stored entries:\n",
       "  1.5   -0.25    ⋅      ⋅ \n",
       " -0.25   1.5   -0.25    ⋅ \n",
       "   ⋅    -0.25   1.5   -0.25\n",
       "   ⋅      ⋅    -0.25   1.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @show T_Euler[:, :]\n",
    "# plot(x, x.*(x))\n",
    "\n",
    "@show A"
   ]
  }
 ],
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